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Equilibrium under TWAP trading with quadratic transaction costs

We study how transaction cost affects to the equilibrium return and optimal stock holdings in equilibrium. To this end, we develop a continuous-time risk-sharing model where heterogenous agents trade toward terminal target holdings subject to a quadratic transaction cost. The equilibrium stock holdings and trading rate under transaction cost are characterized by a unique solution to a forward-backward stochastic differential equation (FBSDE). The equilibrium return is also characterized as the unique solution of a system of coupled but linear FBSDEs.

q-fin.MF↗

Transmission of market orders through communication line with relativistic delay

The notion of "relativistic finance" became ingrained in public imagination and has been asserted in many mass-media reports. Yet, despite an observed drive of the most reputable Wall Street firms to establish their servers ever closer to the trading hubs, there is surprisingly little "hard" information related to relativistic delay of the trading orders. In this paper, the author uses modified M/M/G queue theory to describe propagation of the trading signal with finite velocity.

q-fin.TR↗

Adaptive trading strategies across liquidity pools

In this article, we provide a flexible framework for optimal trading in an asset listed on different venues. We take into account the dependencies between the imbalance and spread of the venues, and allow for partial execution of limit orders at different limits as well as market orders. We present a Bayesian update of the model parameters to take into account possibly changing market conditions and propose extensions to include short/long trading signals, market impact or hidden liquidity. To solve the stochastic control problem of the trader we apply the finite difference method and also develop a deep reinforcement learning algorithm allowing to consider more complex settings.

q-fin.TR↗

Fast Agent-Based Simulation Framework with Applications to Reinforcement Learning and the Study of Trading Latency Effects

We introduce a new software toolbox for agent-based simulation. Facilitating rapid prototyping by offering a user-friendly Python API, its core rests on an efficient C++ implementation to support simulation of large-scale multi-agent systems. Our software environment benefits from a versatile message-driven architecture. Originally developed to support research on financial markets, it offers the flexibility to simulate a wide-range of different (easily customisable) market rules and to study the effect of auxiliary factors, such as delays, on the market dynamics. As a simple illustration, we employ our toolbox to investigate the role of the order processing delay in normal trading and for the scenario of a significant price change. Owing to its general architecture, our toolbox can also be employed as a generic multi-agent system simulator. We provide an example of such a non-financial application by simulating a mechanism for the coordination of no-regret learning agents in a multi-agent network routing scenario previously proposed in the literature.

q-fin.CP↗

DeepFolio: Convolutional Neural Networks for Portfolios with Limit Order Book Data

This work proposes DeepFolio, a new model for deep portfolio management based on data from limit order books (LOB). DeepFolio solves problems found in the state-of-the-art for LOB data to predict price movements. Our evaluation consists of two scenarios using a large dataset of millions of time series. The improvements deliver superior results both in cases of abundant as well as scarce data. The experiments show that DeepFolio outperforms the state-of-the-art on the benchmark FI-2010 LOB. Further, we use DeepFolio for optimal portfolio allocation of crypto-assets with rebalancing. For this purpose, we use two loss-functions - Sharpe ratio loss and minimum volatility risk. We show that DeepFolio outperforms widely used portfolio allocation techniques in the literature.

cs.LG↗

An approximate solution for options market-making in high dimension

Managing a book of options on several underlying involves controlling positions of several thousands of financial assets. It is one of the most challenging financial problems involving both pricing and microstructural modeling. An options market maker has to manage both long- and short-dated options having very different dynamics. In particular, short-dated options inventories cannot be managed as a part of an aggregated inventory, which prevents the use of dimensionality reduction techniques such as a factorial approach or first-order Greeks approximation. In this paper, we show that a simple analytical approximation of the solution of the market maker's problem provides significantly higher flexibility than the existing algorithms designing options market making strategies.

q-fin.TR↗

Automated Market Makers for Decentralized Finance (DeFi)

This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good model for Decentralized Finance (DeFi) applications, LS-LMSR has several advantages over constant product/mean based automated market makers. However, LS-LMSR requires complicated computation (i.e., logarithm and exponentiation) and the cost function curve is concave. In certain DeFi applications, it is preferred to have computationally efficient cost functions with convex curves to conform with the principle of supply and demand. This paper proposes and analyzes constant circle/ellipse based cost functions for automated market makers. The proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have several advantages over widely deployed constant product cost functions. For example, the proposed market makers are more robust against front-runner (slippage) attacks.

q-fin.TR↗

Limit Order Book (LOB) shape modeling in presence of heterogeneously informed market participants

The modeling of the limit order book is directly related to the assumptions on the behavior of real market participants. This paper is twofold. We first present empirical findings that lay the ground for two improvements to these models.The first one is concerned with market participants by adding the additional dimension of informed market makers, whereas the second, and maybe more original one, addresses the race in the book between informed traders and informed market makers leading to different shapes of the order book. Namely we build an agent-based model for the order book with four types of market participants: informed trader, noise trader, informed market makers and noise market makers. We build our model based on the Glosten-Milgrom approach and the most recent Huang-Rosenbaum-Saliba approach. We introduce a parameter capturing the race between informed liquidity traders and suppliers after a new information on the fundamental value of the asset. We then derive the whole 'static' limit order book and its characteristics -- namely the bid-ask spread and volumes available at each level price -- from the interactions between the agents and compare it with the pre-existing model. We then discuss the case where noise traders have an impact on the fundamental value of the asset and extend the model to take into account many kinds of informed market makers.

q-fin.TR↗

Price formation and optimal trading in intraday electricity markets

We develop a tractable equilibrium model for price formation in intraday electricity markets in the presence of intermittent renewable generation. Using stochastic control theory, we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in closed form for a finite number of agents as well as in the asymptotic framework of mean field games. Our model reproduces the empirical features of intraday market prices, such as increasing price volatility at the approach of the delivery date and the correlation between price and renewable infeed forecasts, and relates these features with market characteristics like liquidity, number of agents, and imbalance penalty.

q-fin.PR↗

Optimal market making under partial information and numerical methods for impulse control games with applications

The topics treated in this thesis are inherently two-fold. The first part considers the problem of a market maker optimally setting bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes, but also on unobservable factors modelled by a hidden Markov chain. This stochastic control problem under partial information is solved by means of stochastic filtering, control and PDMPs theory. The value function is characterized as the unique continuous viscosity solution of its dynamic programming equation and numerically compared with its full information counterpart. The optimal full information spreads are shown to be biased when the exact market regime is unknown, as the market maker needs to adjust for additional regime uncertainty in terms of PnL sensitivity and observable order flow volatility. The second part deals with numerically solving nonzero-sum stochastic impulse control games. These offer a realistic and far-reaching modelling framework, but the difficulty in solving such problems has hindered their proliferation. A policy-iteration-type solver is proposed to solve an underlying system of quasi-variational inequalities, and it is validated numerically with reassuring results. Eventually, the focus is put on games with a symmetric structure and an improved algorithm is put forward. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. The algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise too challenging problems, and even some for which results go beyond the scope of the currently available theory.

math.OC↗

Which Trading Agent is Best? Using a Threaded Parallel Simulation of a Financial Market Changes the Pecking-Order

This paper presents novel results generated from a new simulation model of a contemporary financial market, that cast serious doubt on the previously widely accepted view of the relative performance of various well-known public-domain automated-trading algorithms. Various public-domain trading algorithms have been proposed over the past 25 years in a kind of arms-race, where each new trading algorithm was compared to the previous best, thereby establishing a "pecking order", i.e. a partially-ordered dominance hierarchy from best to worst of the various trading algorithms. Many of these algorithms were developed and tested using simple minimal simulations of financial markets that only weakly approximated the fact that real markets involve many different trading systems operating asynchronously and in parallel. In this paper we use BSE, a public-domain market simulator, to run a set of experiments generating benchmark results from several well-known trading algorithms. BSE incorporates a very simple time-sliced approach to simulating parallelism, which has obvious known weaknesses. We then alter and extend BSE to make it threaded, so that different trader algorithms operate asynchronously and in parallel: we call this simulator Threaded-BSE (TBSE). We then re-run the trader experiments on TBSE and compare the TBSE results to our earlier benchmark results from BSE. Our comparison shows that the dominance hierarchy in our more realistic experiments is different from the one given by the original simple simulator. We conclude that simulated parallelism matters a lot, and that earlier results from simple simulations comparing different trader algorithms are no longer to be entirely trusted.

q-fin.TR↗

Optimal Bidding Strategy for Maker Auctions

The Maker Protocol is a decentralized finance application that enables collateralized lending. The application uses open-bid, second-price auctions to complete its loan liquidation process. In this paper, we develop a bidding function for these auctions, focusing on the costs incurred to participate in the auctions. We then optimize these costs using parameters from historical auction data, and compare our optimal bidding prices to the historical auction prices. We find that the majority of auctions end at higher prices than our recommended optimal prices, and we propose several theories for these results.

q-fin.TR↗

Optimal Order Execution in Intraday Markets: Minimizing Costs in Trade Trajectories

Optimal execution, i.e., the determination of the most cost-effective way to trade volumes in continuous trading sessions, has been a topic of interest in the equity trading world for years. Electricity intraday trading slowly follows this trend but is far from being well-researched. The underlying problem is a very complex one. Energy traders, producers, and electricity wholesale companies receive various position updates from customer businesses, renewable energy production, or plant outages and need to trade these positions in intraday markets. They have a variety of options when it comes to position sizing or timing. Is it better to trade all amounts at once? Should they split orders into smaller pieces? Taking the German continuous hourly intraday market as an example, this paper derives an appropriate model for electricity trading. We present our results from an out-of-sample study and differentiate between simple benchmark models and our more refined optimization approach that takes into account order book depth, time to delivery, and different trading regimes like XBID (Cross-Border Intraday Project) trading. Our paper is highly relevant as it contributes further insight into the academic discussion of algorithmic execution in continuous intraday markets and serves as an orientation for practitioners. Our initial results suggest that optimal execution strategies have a considerable monetary impact.

q-fin.TR↗

A bounded operator approach to technical indicators without lag

In the framework of technical analysis for algorithmic trading we use a linear algebra approach in order to define classical technical indicators as bounded operators of the space $l^\infty(\mathbb{N})$. This more abstract view enables us to define in a very simple way the no-lag versions of these tools. Then we apply our results to a basic trading system in order to compare the classical Elder's impulse system with its no-lag version and the so-called Nyquist-Elder's impulse system.

q-fin.TR↗

A Time Series Data Analysis of Indian Commercial Dynamism

In this report it is analyzed the focuses of the commercial dynamism of India, covering the fundamentals of growth rate, trade balance, coverage rate, openness rate, share of world indicators and then present each of them in detail.

q-fin.TR↗

A Generic Methodology for the Statistically Uniform & Comparable Evaluation of Automated Trading Platform Components

Although machine learning approaches have been widely used in the field of finance, to very successful degrees, these approaches remain bespoke to specific investigations and opaque in terms of explainability, comparability, and reproducibility. The primary objective of this research was to shed light upon this field by providing a generic methodology that was investigation-agnostic and interpretable to a financial markets practitioner, thus enhancing their efficiency, reducing barriers to entry, and increasing the reproducibility of experiments. The proposed methodology is showcased on two automated trading platform components. Namely, price levels, a well-known trading pattern, and a novel 2-step feature extraction method. The methodology relies on hypothesis testing, which is widely applied in other social and scientific disciplines to effectively evaluate the concrete results beyond simple classification accuracy. The main hypothesis was formulated to evaluate whether the selected trading pattern is suitable for use in the machine learning setting. Across the experiments we found that the use of the considered trading pattern in the machine learning setting is only partially supported by statistics, resulting in insignificant effect sizes (Rebound 7 - $0.64 \pm 1.02$, Rebound 11 $0.38 \pm 0.98$, and rebound 15 - $1.05 \pm 1.16$), but allowed the rejection of the null hypothesis. We showcased the generic methodology on a US futures market instrument and provided evidence that with this methodology we could easily obtain informative metrics beyond the more traditional performance and profitability metrics. This work is one of the first in applying this rigorous statistically-backed approach to the field of financial markets and we hope this may be a springboard for more research.

q-fin.TR↗

On Detecting Spoofing Strategies in High Frequency Trading

Spoofing is an illegal act of artificially modifying the supply to drive temporarily prices in a given direction for profit. In practice, detection of such an act is challenging due to the complexity of modern electronic platforms and the high frequency at which orders are channeled. We present a micro-structural study of spoofing in a simple static setting. A multilevel imbalance which influences the resulting price movement is introduced upon which we describe the optimization strategy of a potential spoofer. We provide conditions under which a market is more likely to admit spoofing behavior as a function of the characteristics of the market. We describe the optimal spoofing strategy after optimization which allows us to quantify the resulting impact on the imbalance after spoofing. Based on these results we calibrate the model to real Level 2 datasets from TMX, and provide some monitoring procedures based on the Wasserstein distance to detect spoofing strategies in real time.

q-fin.TR↗

Gold Standard Pairs Trading Rules: Are They Valid?

Pairs trading is a strategy based on exploiting mean reversion in prices of securities. It has been shown to generate significant excess returns, but its profitability has dropped significantly in recent periods. We employ the most common distance and cointegration methods on US equities from 1990 to 2020 including the Covid-19 crisis. The strategy overall fails to outperform the market benchmark even with hyperparameter tuning, but it performs very strongly during bear markets. Furthermore, we demonstrate that market factors have a strong relationship with the optimal parametrization for the strategy, and adjustments are appropriate for modern market conditions.

q-fin.TR↗